2020/12/10 by Spitz, Daniel, Wienhard, Anna
#FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.2012.05751
Persistent homology provides a robust methodology to infer topological structures from point cloud data. Here we explore the persistent homology of point clouds embedded into a probabilistic setting, exploiting the theory of point processes. We introduce measures on the space of persistence diagrams and the self-similar scaling of a one-parameter family of these. As the main result we prove a packing relation between the occurring scaling exponents.